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On the exact asymptotics of the busy period in GI/G/1 queues

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Zbigniew Palmowski  and
Tomasz Rolski
Zbigniew Palmowski*
Affiliation:
Wrocław University and Utrecht University
Tomasz Rolski*
Affiliation:
Wrocław University
*
∗ Postal address: Mathematical Institute, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
∗ Postal address: Mathematical Institute, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
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Abstract

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In this paper we study the busy period in GI/G/1 work-conserving queues. We give the exact asymptotics of the tail distribution of the busy period under the light tail assumptions. We also study the workload process in the M/G/1 system conditioned to stay positive.

Keywords

GI/G/1 queuebusy periodworkload process conditioned to stay positiveexponential change of measurequasistationary distributionexact asymptoticse

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J35: Transition functions, generators and resolvents
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 3 , September 2006 , pp. 792 - 803
Copyright
Copyright © Applied Probability Trust 2006 

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